Analysis of Three-Dimensional DC Magnetron Discharge by the Particle-in-Cell/Monte Carlo Method

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Abstract
The structure of a three-dimensional dc magnetron discharge is clarified by the use of the PIC/MC method. Magnets are placed in the form of a racetrack with the practical dimensions of a commercial sputtering apparatus. The cathode sheath has a three-dimensional structure; the sheath is thinnest in the midst of magnets. As the magnetic field B increases in strength, the sheath thickness decreases. The similarity law for the sheath thickness proposed by Gu and Lieberman [J. Vac. Sci. Technol. A 16 (1988) 2960] works well. The plasma density peaks outside the sheath. As B increases, the location of the peak moves closer to the cathode and the plasma is more widely distributed between the electrodes. The distribution of the peak plasma density on the plane parallel to the electrode has a strong correlation with the distribution of ion flux onto the cathode. Pressure has little effect on the electric field. However, as pressure decreases, the plasma density exhibits a wider distribution.